Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8035,2,Mod(1,8035)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8035, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("8035.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8035 = 5 \cdot 1607 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8035.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(64.1597980241\) |
Analytic rank: | \(1\) |
Dimension: | \(114\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.19 | ||
Character | \(\chi\) | \(=\) | 8035.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.12278 | −1.50103 | −0.750517 | − | 0.660851i | \(-0.770196\pi\) | ||||
−0.750517 | + | 0.660851i | \(0.770196\pi\) | |||||||
\(3\) | −3.22748 | −1.86339 | −0.931694 | − | 0.363244i | \(-0.881669\pi\) | ||||
−0.931694 | + | 0.363244i | \(0.881669\pi\) | |||||||
\(4\) | 2.50621 | 1.25311 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | 6.85125 | 2.79701 | ||||||||
\(7\) | 1.25827 | 0.475580 | 0.237790 | − | 0.971317i | \(-0.423577\pi\) | ||||
0.237790 | + | 0.971317i | \(0.423577\pi\) | |||||||
\(8\) | −1.07458 | −0.379920 | ||||||||
\(9\) | 7.41664 | 2.47221 | ||||||||
\(10\) | −2.12278 | −0.671283 | ||||||||
\(11\) | −5.28754 | −1.59425 | −0.797126 | − | 0.603813i | \(-0.793648\pi\) | ||||
−0.797126 | + | 0.603813i | \(0.793648\pi\) | |||||||
\(12\) | −8.08875 | −2.33502 | ||||||||
\(13\) | −5.41589 | −1.50210 | −0.751048 | − | 0.660247i | \(-0.770451\pi\) | ||||
−0.751048 | + | 0.660247i | \(0.770451\pi\) | |||||||
\(14\) | −2.67103 | −0.713862 | ||||||||
\(15\) | −3.22748 | −0.833332 | ||||||||
\(16\) | −2.73133 | −0.682832 | ||||||||
\(17\) | 0.0963515 | 0.0233687 | 0.0116843 | − | 0.999932i | \(-0.496281\pi\) | ||||
0.0116843 | + | 0.999932i | \(0.496281\pi\) | |||||||
\(18\) | −15.7439 | −3.71088 | ||||||||
\(19\) | 1.09592 | 0.251421 | 0.125710 | − | 0.992067i | \(-0.459879\pi\) | ||||
0.125710 | + | 0.992067i | \(0.459879\pi\) | |||||||
\(20\) | 2.50621 | 0.560406 | ||||||||
\(21\) | −4.06103 | −0.886189 | ||||||||
\(22\) | 11.2243 | 2.39303 | ||||||||
\(23\) | 2.58108 | 0.538192 | 0.269096 | − | 0.963113i | \(-0.413275\pi\) | ||||
0.269096 | + | 0.963113i | \(0.413275\pi\) | |||||||
\(24\) | 3.46818 | 0.707938 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 11.4968 | 2.25470 | ||||||||
\(27\) | −14.2546 | −2.74331 | ||||||||
\(28\) | 3.15348 | 0.595951 | ||||||||
\(29\) | −9.69197 | −1.79975 | −0.899877 | − | 0.436143i | \(-0.856344\pi\) | ||||
−0.899877 | + | 0.436143i | \(0.856344\pi\) | |||||||
\(30\) | 6.85125 | 1.25086 | ||||||||
\(31\) | −5.73717 | −1.03043 | −0.515213 | − | 0.857062i | \(-0.672287\pi\) | ||||
−0.515213 | + | 0.857062i | \(0.672287\pi\) | |||||||
\(32\) | 7.94717 | 1.40487 | ||||||||
\(33\) | 17.0654 | 2.97071 | ||||||||
\(34\) | −0.204533 | −0.0350772 | ||||||||
\(35\) | 1.25827 | 0.212686 | ||||||||
\(36\) | 18.5877 | 3.09795 | ||||||||
\(37\) | 7.95947 | 1.30853 | 0.654264 | − | 0.756266i | \(-0.272978\pi\) | ||||
0.654264 | + | 0.756266i | \(0.272978\pi\) | |||||||
\(38\) | −2.32640 | −0.377391 | ||||||||
\(39\) | 17.4797 | 2.79899 | ||||||||
\(40\) | −1.07458 | −0.169905 | ||||||||
\(41\) | 0.183699 | 0.0286889 | 0.0143444 | − | 0.999897i | \(-0.495434\pi\) | ||||
0.0143444 | + | 0.999897i | \(0.495434\pi\) | |||||||
\(42\) | 8.62069 | 1.33020 | ||||||||
\(43\) | 8.82458 | 1.34574 | 0.672868 | − | 0.739762i | \(-0.265062\pi\) | ||||
0.672868 | + | 0.739762i | \(0.265062\pi\) | |||||||
\(44\) | −13.2517 | −1.99777 | ||||||||
\(45\) | 7.41664 | 1.10561 | ||||||||
\(46\) | −5.47907 | −0.807845 | ||||||||
\(47\) | 11.1082 | 1.62030 | 0.810150 | − | 0.586223i | \(-0.199386\pi\) | ||||
0.810150 | + | 0.586223i | \(0.199386\pi\) | |||||||
\(48\) | 8.81532 | 1.27238 | ||||||||
\(49\) | −5.41677 | −0.773824 | ||||||||
\(50\) | −2.12278 | −0.300207 | ||||||||
\(51\) | −0.310973 | −0.0435449 | ||||||||
\(52\) | −13.5734 | −1.88229 | ||||||||
\(53\) | 4.26606 | 0.585989 | 0.292994 | − | 0.956114i | \(-0.405348\pi\) | ||||
0.292994 | + | 0.956114i | \(0.405348\pi\) | |||||||
\(54\) | 30.2595 | 4.11780 | ||||||||
\(55\) | −5.28754 | −0.712972 | ||||||||
\(56\) | −1.35210 | −0.180682 | ||||||||
\(57\) | −3.53706 | −0.468495 | ||||||||
\(58\) | 20.5740 | 2.70149 | ||||||||
\(59\) | −0.728348 | −0.0948228 | −0.0474114 | − | 0.998875i | \(-0.515097\pi\) | ||||
−0.0474114 | + | 0.998875i | \(0.515097\pi\) | |||||||
\(60\) | −8.08875 | −1.04425 | ||||||||
\(61\) | 0.00924476 | 0.00118367 | 0.000591835 | − | 1.00000i | \(-0.499812\pi\) | ||||
0.000591835 | 1.00000i | \(0.499812\pi\) | ||||||||
\(62\) | 12.1788 | 1.54671 | ||||||||
\(63\) | 9.33211 | 1.17573 | ||||||||
\(64\) | −11.4075 | −1.42593 | ||||||||
\(65\) | −5.41589 | −0.671758 | ||||||||
\(66\) | −36.2262 | −4.45914 | ||||||||
\(67\) | −3.46467 | −0.423277 | −0.211639 | − | 0.977348i | \(-0.567880\pi\) | ||||
−0.211639 | + | 0.977348i | \(0.567880\pi\) | |||||||
\(68\) | 0.241477 | 0.0292834 | ||||||||
\(69\) | −8.33039 | −1.00286 | ||||||||
\(70\) | −2.67103 | −0.319249 | ||||||||
\(71\) | −7.12503 | −0.845586 | −0.422793 | − | 0.906226i | \(-0.638950\pi\) | ||||
−0.422793 | + | 0.906226i | \(0.638950\pi\) | |||||||
\(72\) | −7.96975 | −0.939244 | ||||||||
\(73\) | −7.57368 | −0.886432 | −0.443216 | − | 0.896415i | \(-0.646163\pi\) | ||||
−0.443216 | + | 0.896415i | \(0.646163\pi\) | |||||||
\(74\) | −16.8962 | −1.96415 | ||||||||
\(75\) | −3.22748 | −0.372678 | ||||||||
\(76\) | 2.74660 | 0.315057 | ||||||||
\(77\) | −6.65313 | −0.758194 | ||||||||
\(78\) | −37.1056 | −4.20138 | ||||||||
\(79\) | 15.5923 | 1.75427 | 0.877136 | − | 0.480241i | \(-0.159451\pi\) | ||||
0.877136 | + | 0.480241i | \(0.159451\pi\) | |||||||
\(80\) | −2.73133 | −0.305372 | ||||||||
\(81\) | 23.7567 | 2.63963 | ||||||||
\(82\) | −0.389952 | −0.0430630 | ||||||||
\(83\) | 10.1024 | 1.10889 | 0.554444 | − | 0.832221i | \(-0.312931\pi\) | ||||
0.554444 | + | 0.832221i | \(0.312931\pi\) | |||||||
\(84\) | −10.1778 | −1.11049 | ||||||||
\(85\) | 0.0963515 | 0.0104508 | ||||||||
\(86\) | −18.7327 | −2.02000 | ||||||||
\(87\) | 31.2807 | 3.35364 | ||||||||
\(88\) | 5.68186 | 0.605688 | ||||||||
\(89\) | 6.85878 | 0.727030 | 0.363515 | − | 0.931588i | \(-0.381577\pi\) | ||||
0.363515 | + | 0.931588i | \(0.381577\pi\) | |||||||
\(90\) | −15.7439 | −1.65956 | ||||||||
\(91\) | −6.81462 | −0.714366 | ||||||||
\(92\) | 6.46873 | 0.674412 | ||||||||
\(93\) | 18.5166 | 1.92008 | ||||||||
\(94\) | −23.5803 | −2.43213 | ||||||||
\(95\) | 1.09592 | 0.112439 | ||||||||
\(96\) | −25.6494 | −2.61783 | ||||||||
\(97\) | 2.35225 | 0.238835 | 0.119418 | − | 0.992844i | \(-0.461897\pi\) | ||||
0.119418 | + | 0.992844i | \(0.461897\pi\) | |||||||
\(98\) | 11.4986 | 1.16154 | ||||||||
\(99\) | −39.2158 | −3.94133 | ||||||||
\(100\) | 2.50621 | 0.250621 | ||||||||
\(101\) | −2.37026 | −0.235850 | −0.117925 | − | 0.993023i | \(-0.537624\pi\) | ||||
−0.117925 | + | 0.993023i | \(0.537624\pi\) | |||||||
\(102\) | 0.660128 | 0.0653624 | ||||||||
\(103\) | 16.8025 | 1.65560 | 0.827800 | − | 0.561024i | \(-0.189592\pi\) | ||||
0.827800 | + | 0.561024i | \(0.189592\pi\) | |||||||
\(104\) | 5.81978 | 0.570677 | ||||||||
\(105\) | −4.06103 | −0.396316 | ||||||||
\(106\) | −9.05593 | −0.879590 | ||||||||
\(107\) | −16.2024 | −1.56635 | −0.783173 | − | 0.621804i | \(-0.786400\pi\) | ||||
−0.783173 | + | 0.621804i | \(0.786400\pi\) | |||||||
\(108\) | −35.7251 | −3.43765 | ||||||||
\(109\) | −14.4627 | −1.38528 | −0.692638 | − | 0.721286i | \(-0.743552\pi\) | ||||
−0.692638 | + | 0.721286i | \(0.743552\pi\) | |||||||
\(110\) | 11.2243 | 1.07020 | ||||||||
\(111\) | −25.6890 | −2.43830 | ||||||||
\(112\) | −3.43674 | −0.324741 | ||||||||
\(113\) | −5.31068 | −0.499586 | −0.249793 | − | 0.968299i | \(-0.580363\pi\) | ||||
−0.249793 | + | 0.968299i | \(0.580363\pi\) | |||||||
\(114\) | 7.50841 | 0.703227 | ||||||||
\(115\) | 2.58108 | 0.240687 | ||||||||
\(116\) | −24.2901 | −2.25528 | ||||||||
\(117\) | −40.1677 | −3.71351 | ||||||||
\(118\) | 1.54612 | 0.142332 | ||||||||
\(119\) | 0.121236 | 0.0111137 | ||||||||
\(120\) | 3.46818 | 0.316600 | ||||||||
\(121\) | 16.9581 | 1.54164 | ||||||||
\(122\) | −0.0196246 | −0.00177673 | ||||||||
\(123\) | −0.592884 | −0.0534585 | ||||||||
\(124\) | −14.3786 | −1.29123 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | −19.8100 | −1.76482 | ||||||||
\(127\) | −1.86927 | −0.165871 | −0.0829353 | − | 0.996555i | \(-0.526429\pi\) | ||||
−0.0829353 | + | 0.996555i | \(0.526429\pi\) | |||||||
\(128\) | 8.32125 | 0.735501 | ||||||||
\(129\) | −28.4812 | −2.50763 | ||||||||
\(130\) | 11.4968 | 1.00833 | ||||||||
\(131\) | −11.5178 | −1.00631 | −0.503156 | − | 0.864196i | \(-0.667828\pi\) | ||||
−0.503156 | + | 0.864196i | \(0.667828\pi\) | |||||||
\(132\) | 42.7696 | 3.72261 | ||||||||
\(133\) | 1.37896 | 0.119571 | ||||||||
\(134\) | 7.35475 | 0.635353 | ||||||||
\(135\) | −14.2546 | −1.22684 | ||||||||
\(136\) | −0.103537 | −0.00887823 | ||||||||
\(137\) | −0.667543 | −0.0570320 | −0.0285160 | − | 0.999593i | \(-0.509078\pi\) | ||||
−0.0285160 | + | 0.999593i | \(0.509078\pi\) | |||||||
\(138\) | 17.6836 | 1.50533 | ||||||||
\(139\) | 8.98399 | 0.762012 | 0.381006 | − | 0.924573i | \(-0.375578\pi\) | ||||
0.381006 | + | 0.924573i | \(0.375578\pi\) | |||||||
\(140\) | 3.15348 | 0.266518 | ||||||||
\(141\) | −35.8516 | −3.01925 | ||||||||
\(142\) | 15.1249 | 1.26925 | ||||||||
\(143\) | 28.6367 | 2.39472 | ||||||||
\(144\) | −20.2573 | −1.68811 | ||||||||
\(145\) | −9.69197 | −0.804875 | ||||||||
\(146\) | 16.0773 | 1.33057 | ||||||||
\(147\) | 17.4825 | 1.44193 | ||||||||
\(148\) | 19.9481 | 1.63972 | ||||||||
\(149\) | 21.2490 | 1.74078 | 0.870392 | − | 0.492359i | \(-0.163865\pi\) | ||||
0.870392 | + | 0.492359i | \(0.163865\pi\) | |||||||
\(150\) | 6.85125 | 0.559402 | ||||||||
\(151\) | −2.90523 | −0.236425 | −0.118212 | − | 0.992988i | \(-0.537716\pi\) | ||||
−0.118212 | + | 0.992988i | \(0.537716\pi\) | |||||||
\(152\) | −1.17765 | −0.0955198 | ||||||||
\(153\) | 0.714605 | 0.0577724 | ||||||||
\(154\) | 14.1231 | 1.13808 | ||||||||
\(155\) | −5.73717 | −0.460821 | ||||||||
\(156\) | 43.8078 | 3.50743 | ||||||||
\(157\) | −10.6639 | −0.851071 | −0.425535 | − | 0.904942i | \(-0.639914\pi\) | ||||
−0.425535 | + | 0.904942i | \(0.639914\pi\) | |||||||
\(158\) | −33.0991 | −2.63322 | ||||||||
\(159\) | −13.7686 | −1.09192 | ||||||||
\(160\) | 7.94717 | 0.628279 | ||||||||
\(161\) | 3.24768 | 0.255953 | ||||||||
\(162\) | −50.4303 | −3.96218 | ||||||||
\(163\) | 12.3766 | 0.969407 | 0.484703 | − | 0.874679i | \(-0.338928\pi\) | ||||
0.484703 | + | 0.874679i | \(0.338928\pi\) | |||||||
\(164\) | 0.460387 | 0.0359502 | ||||||||
\(165\) | 17.0654 | 1.32854 | ||||||||
\(166\) | −21.4453 | −1.66448 | ||||||||
\(167\) | −15.6367 | −1.21001 | −0.605004 | − | 0.796223i | \(-0.706828\pi\) | ||||
−0.605004 | + | 0.796223i | \(0.706828\pi\) | |||||||
\(168\) | 4.36388 | 0.336681 | ||||||||
\(169\) | 16.3318 | 1.25629 | ||||||||
\(170\) | −0.204533 | −0.0156870 | ||||||||
\(171\) | 8.12803 | 0.621566 | ||||||||
\(172\) | 22.1163 | 1.68635 | ||||||||
\(173\) | −11.0772 | −0.842187 | −0.421093 | − | 0.907017i | \(-0.638354\pi\) | ||||
−0.421093 | + | 0.907017i | \(0.638354\pi\) | |||||||
\(174\) | −66.4021 | −5.03393 | ||||||||
\(175\) | 1.25827 | 0.0951159 | ||||||||
\(176\) | 14.4420 | 1.08861 | ||||||||
\(177\) | 2.35073 | 0.176692 | ||||||||
\(178\) | −14.5597 | −1.09130 | ||||||||
\(179\) | 11.3970 | 0.851851 | 0.425925 | − | 0.904758i | \(-0.359949\pi\) | ||||
0.425925 | + | 0.904758i | \(0.359949\pi\) | |||||||
\(180\) | 18.5877 | 1.38544 | ||||||||
\(181\) | 6.95468 | 0.516938 | 0.258469 | − | 0.966020i | \(-0.416782\pi\) | ||||
0.258469 | + | 0.966020i | \(0.416782\pi\) | |||||||
\(182\) | 14.4660 | 1.07229 | ||||||||
\(183\) | −0.0298373 | −0.00220564 | ||||||||
\(184\) | −2.77357 | −0.204470 | ||||||||
\(185\) | 7.95947 | 0.585192 | ||||||||
\(186\) | −39.3068 | −2.88211 | ||||||||
\(187\) | −0.509462 | −0.0372556 | ||||||||
\(188\) | 27.8395 | 2.03041 | ||||||||
\(189\) | −17.9361 | −1.30466 | ||||||||
\(190\) | −2.32640 | −0.168775 | ||||||||
\(191\) | 4.90468 | 0.354890 | 0.177445 | − | 0.984131i | \(-0.443217\pi\) | ||||
0.177445 | + | 0.984131i | \(0.443217\pi\) | |||||||
\(192\) | 36.8174 | 2.65707 | ||||||||
\(193\) | 3.12752 | 0.225124 | 0.112562 | − | 0.993645i | \(-0.464094\pi\) | ||||
0.112562 | + | 0.993645i | \(0.464094\pi\) | |||||||
\(194\) | −4.99332 | −0.358500 | ||||||||
\(195\) | 17.4797 | 1.25175 | ||||||||
\(196\) | −13.5756 | −0.969683 | ||||||||
\(197\) | −15.1557 | −1.07980 | −0.539899 | − | 0.841730i | \(-0.681537\pi\) | ||||
−0.539899 | + | 0.841730i | \(0.681537\pi\) | |||||||
\(198\) | 83.2466 | 5.91608 | ||||||||
\(199\) | 22.9484 | 1.62677 | 0.813385 | − | 0.581725i | \(-0.197622\pi\) | ||||
0.813385 | + | 0.581725i | \(0.197622\pi\) | |||||||
\(200\) | −1.07458 | −0.0759840 | ||||||||
\(201\) | 11.1822 | 0.788729 | ||||||||
\(202\) | 5.03156 | 0.354019 | ||||||||
\(203\) | −12.1951 | −0.855926 | ||||||||
\(204\) | −0.779364 | −0.0545664 | ||||||||
\(205\) | 0.183699 | 0.0128301 | ||||||||
\(206\) | −35.6681 | −2.48511 | ||||||||
\(207\) | 19.1429 | 1.33053 | ||||||||
\(208\) | 14.7926 | 1.02568 | ||||||||
\(209\) | −5.79471 | −0.400828 | ||||||||
\(210\) | 8.62069 | 0.594884 | ||||||||
\(211\) | 2.35450 | 0.162091 | 0.0810453 | − | 0.996710i | \(-0.474174\pi\) | ||||
0.0810453 | + | 0.996710i | \(0.474174\pi\) | |||||||
\(212\) | 10.6917 | 0.734306 | ||||||||
\(213\) | 22.9959 | 1.57565 | ||||||||
\(214\) | 34.3942 | 2.35114 | ||||||||
\(215\) | 8.82458 | 0.601832 | ||||||||
\(216\) | 15.3177 | 1.04224 | ||||||||
\(217\) | −7.21888 | −0.490050 | ||||||||
\(218\) | 30.7012 | 2.07935 | ||||||||
\(219\) | 24.4439 | 1.65177 | ||||||||
\(220\) | −13.2517 | −0.893428 | ||||||||
\(221\) | −0.521829 | −0.0351020 | ||||||||
\(222\) | 54.5323 | 3.65997 | ||||||||
\(223\) | 11.5823 | 0.775607 | 0.387803 | − | 0.921742i | \(-0.373234\pi\) | ||||
0.387803 | + | 0.921742i | \(0.373234\pi\) | |||||||
\(224\) | 9.99965 | 0.668130 | ||||||||
\(225\) | 7.41664 | 0.494443 | ||||||||
\(226\) | 11.2734 | 0.749896 | ||||||||
\(227\) | −9.71403 | −0.644743 | −0.322371 | − | 0.946613i | \(-0.604480\pi\) | ||||
−0.322371 | + | 0.946613i | \(0.604480\pi\) | |||||||
\(228\) | −8.86461 | −0.587073 | ||||||||
\(229\) | 2.57391 | 0.170089 | 0.0850444 | − | 0.996377i | \(-0.472897\pi\) | ||||
0.0850444 | + | 0.996377i | \(0.472897\pi\) | |||||||
\(230\) | −5.47907 | −0.361279 | ||||||||
\(231\) | 21.4728 | 1.41281 | ||||||||
\(232\) | 10.4148 | 0.683763 | ||||||||
\(233\) | −12.3695 | −0.810354 | −0.405177 | − | 0.914238i | \(-0.632790\pi\) | ||||
−0.405177 | + | 0.914238i | \(0.632790\pi\) | |||||||
\(234\) | 85.2673 | 5.57410 | ||||||||
\(235\) | 11.1082 | 0.724620 | ||||||||
\(236\) | −1.82539 | −0.118823 | ||||||||
\(237\) | −50.3239 | −3.26889 | ||||||||
\(238\) | −0.257357 | −0.0166820 | ||||||||
\(239\) | 22.7696 | 1.47284 | 0.736420 | − | 0.676524i | \(-0.236515\pi\) | ||||
0.736420 | + | 0.676524i | \(0.236515\pi\) | |||||||
\(240\) | 8.81532 | 0.569026 | ||||||||
\(241\) | −2.16627 | −0.139542 | −0.0697709 | − | 0.997563i | \(-0.522227\pi\) | ||||
−0.0697709 | + | 0.997563i | \(0.522227\pi\) | |||||||
\(242\) | −35.9983 | −2.31406 | ||||||||
\(243\) | −33.9103 | −2.17535 | ||||||||
\(244\) | 0.0231693 | 0.00148326 | ||||||||
\(245\) | −5.41677 | −0.346065 | ||||||||
\(246\) | 1.25856 | 0.0802431 | ||||||||
\(247\) | −5.93537 | −0.377658 | ||||||||
\(248\) | 6.16503 | 0.391480 | ||||||||
\(249\) | −32.6055 | −2.06629 | ||||||||
\(250\) | −2.12278 | −0.134257 | ||||||||
\(251\) | −12.4537 | −0.786069 | −0.393035 | − | 0.919524i | \(-0.628575\pi\) | ||||
−0.393035 | + | 0.919524i | \(0.628575\pi\) | |||||||
\(252\) | 23.3882 | 1.47332 | ||||||||
\(253\) | −13.6476 | −0.858015 | ||||||||
\(254\) | 3.96805 | 0.248978 | ||||||||
\(255\) | −0.310973 | −0.0194739 | ||||||||
\(256\) | 5.15073 | 0.321921 | ||||||||
\(257\) | 28.4790 | 1.77647 | 0.888236 | − | 0.459388i | \(-0.151931\pi\) | ||||
0.888236 | + | 0.459388i | \(0.151931\pi\) | |||||||
\(258\) | 60.4594 | 3.76404 | ||||||||
\(259\) | 10.0151 | 0.622310 | ||||||||
\(260\) | −13.5734 | −0.841784 | ||||||||
\(261\) | −71.8819 | −4.44938 | ||||||||
\(262\) | 24.4497 | 1.51051 | ||||||||
\(263\) | −18.2807 | −1.12724 | −0.563618 | − | 0.826035i | \(-0.690591\pi\) | ||||
−0.563618 | + | 0.826035i | \(0.690591\pi\) | |||||||
\(264\) | −18.3381 | −1.12863 | ||||||||
\(265\) | 4.26606 | 0.262062 | ||||||||
\(266\) | −2.92722 | −0.179480 | ||||||||
\(267\) | −22.1366 | −1.35474 | ||||||||
\(268\) | −8.68320 | −0.530411 | ||||||||
\(269\) | 7.29726 | 0.444922 | 0.222461 | − | 0.974942i | \(-0.428591\pi\) | ||||
0.222461 | + | 0.974942i | \(0.428591\pi\) | |||||||
\(270\) | 30.2595 | 1.84154 | ||||||||
\(271\) | 13.1334 | 0.797795 | 0.398897 | − | 0.916996i | \(-0.369393\pi\) | ||||
0.398897 | + | 0.916996i | \(0.369393\pi\) | |||||||
\(272\) | −0.263168 | −0.0159569 | ||||||||
\(273\) | 21.9941 | 1.33114 | ||||||||
\(274\) | 1.41705 | 0.0856070 | ||||||||
\(275\) | −5.28754 | −0.318851 | ||||||||
\(276\) | −20.8777 | −1.25669 | ||||||||
\(277\) | 12.6410 | 0.759526 | 0.379763 | − | 0.925084i | \(-0.376005\pi\) | ||||
0.379763 | + | 0.925084i | \(0.376005\pi\) | |||||||
\(278\) | −19.0711 | −1.14381 | ||||||||
\(279\) | −42.5506 | −2.54744 | ||||||||
\(280\) | −1.35210 | −0.0808035 | ||||||||
\(281\) | −7.16052 | −0.427161 | −0.213580 | − | 0.976925i | \(-0.568513\pi\) | ||||
−0.213580 | + | 0.976925i | \(0.568513\pi\) | |||||||
\(282\) | 76.1051 | 4.53199 | ||||||||
\(283\) | 3.22701 | 0.191826 | 0.0959130 | − | 0.995390i | \(-0.469423\pi\) | ||||
0.0959130 | + | 0.995390i | \(0.469423\pi\) | |||||||
\(284\) | −17.8568 | −1.05961 | ||||||||
\(285\) | −3.53706 | −0.209517 | ||||||||
\(286\) | −60.7895 | −3.59456 | ||||||||
\(287\) | 0.231142 | 0.0136439 | ||||||||
\(288\) | 58.9414 | 3.47315 | ||||||||
\(289\) | −16.9907 | −0.999454 | ||||||||
\(290\) | 20.5740 | 1.20814 | ||||||||
\(291\) | −7.59186 | −0.445042 | ||||||||
\(292\) | −18.9812 | −1.11079 | ||||||||
\(293\) | 4.23600 | 0.247470 | 0.123735 | − | 0.992315i | \(-0.460513\pi\) | ||||
0.123735 | + | 0.992315i | \(0.460513\pi\) | |||||||
\(294\) | −37.1116 | −2.16439 | ||||||||
\(295\) | −0.728348 | −0.0424060 | ||||||||
\(296\) | −8.55305 | −0.497136 | ||||||||
\(297\) | 75.3720 | 4.37352 | ||||||||
\(298\) | −45.1070 | −2.61298 | ||||||||
\(299\) | −13.9788 | −0.808417 | ||||||||
\(300\) | −8.08875 | −0.467004 | ||||||||
\(301\) | 11.1037 | 0.640005 | ||||||||
\(302\) | 6.16718 | 0.354882 | ||||||||
\(303\) | 7.64998 | 0.439480 | ||||||||
\(304\) | −2.99331 | −0.171678 | ||||||||
\(305\) | 0.00924476 | 0.000529354 0 | ||||||||
\(306\) | −1.51695 | −0.0867184 | ||||||||
\(307\) | 2.50213 | 0.142804 | 0.0714019 | − | 0.997448i | \(-0.477253\pi\) | ||||
0.0714019 | + | 0.997448i | \(0.477253\pi\) | |||||||
\(308\) | −16.6741 | −0.950097 | ||||||||
\(309\) | −54.2298 | −3.08502 | ||||||||
\(310\) | 12.1788 | 0.691708 | ||||||||
\(311\) | 7.13749 | 0.404730 | 0.202365 | − | 0.979310i | \(-0.435137\pi\) | ||||
0.202365 | + | 0.979310i | \(0.435137\pi\) | |||||||
\(312\) | −18.7832 | −1.06339 | ||||||||
\(313\) | 16.0884 | 0.909370 | 0.454685 | − | 0.890652i | \(-0.349752\pi\) | ||||
0.454685 | + | 0.890652i | \(0.349752\pi\) | |||||||
\(314\) | 22.6371 | 1.27749 | ||||||||
\(315\) | 9.33211 | 0.525805 | ||||||||
\(316\) | 39.0776 | 2.19829 | ||||||||
\(317\) | 21.5958 | 1.21294 | 0.606472 | − | 0.795105i | \(-0.292584\pi\) | ||||
0.606472 | + | 0.795105i | \(0.292584\pi\) | |||||||
\(318\) | 29.2279 | 1.63902 | ||||||||
\(319\) | 51.2467 | 2.86926 | ||||||||
\(320\) | −11.4075 | −0.637697 | ||||||||
\(321\) | 52.2930 | 2.91871 | ||||||||
\(322\) | −6.89413 | −0.384195 | ||||||||
\(323\) | 0.105593 | 0.00587537 | ||||||||
\(324\) | 59.5392 | 3.30774 | ||||||||
\(325\) | −5.41589 | −0.300419 | ||||||||
\(326\) | −26.2728 | −1.45511 | ||||||||
\(327\) | 46.6781 | 2.58131 | ||||||||
\(328\) | −0.197398 | −0.0108995 | ||||||||
\(329\) | 13.9771 | 0.770581 | ||||||||
\(330\) | −36.2262 | −1.99419 | ||||||||
\(331\) | 15.5622 | 0.855378 | 0.427689 | − | 0.903926i | \(-0.359328\pi\) | ||||
0.427689 | + | 0.903926i | \(0.359328\pi\) | |||||||
\(332\) | 25.3189 | 1.38955 | ||||||||
\(333\) | 59.0325 | 3.23496 | ||||||||
\(334\) | 33.1934 | 1.81626 | ||||||||
\(335\) | −3.46467 | −0.189295 | ||||||||
\(336\) | 11.0920 | 0.605119 | ||||||||
\(337\) | −24.6361 | −1.34201 | −0.671007 | − | 0.741451i | \(-0.734138\pi\) | ||||
−0.671007 | + | 0.741451i | \(0.734138\pi\) | |||||||
\(338\) | −34.6689 | −1.88574 | ||||||||
\(339\) | 17.1401 | 0.930923 | ||||||||
\(340\) | 0.241477 | 0.0130959 | ||||||||
\(341\) | 30.3355 | 1.64276 | ||||||||
\(342\) | −17.2541 | −0.932993 | ||||||||
\(343\) | −15.6236 | −0.843595 | ||||||||
\(344\) | −9.48268 | −0.511272 | ||||||||
\(345\) | −8.33039 | −0.448493 | ||||||||
\(346\) | 23.5146 | 1.26415 | ||||||||
\(347\) | 6.32537 | 0.339564 | 0.169782 | − | 0.985482i | \(-0.445694\pi\) | ||||
0.169782 | + | 0.985482i | \(0.445694\pi\) | |||||||
\(348\) | 78.3960 | 4.20247 | ||||||||
\(349\) | −12.8451 | −0.687581 | −0.343790 | − | 0.939046i | \(-0.611711\pi\) | ||||
−0.343790 | + | 0.939046i | \(0.611711\pi\) | |||||||
\(350\) | −2.67103 | −0.142772 | ||||||||
\(351\) | 77.2015 | 4.12071 | ||||||||
\(352\) | −42.0210 | −2.23973 | ||||||||
\(353\) | 4.23655 | 0.225489 | 0.112744 | − | 0.993624i | \(-0.464036\pi\) | ||||
0.112744 | + | 0.993624i | \(0.464036\pi\) | |||||||
\(354\) | −4.99009 | −0.265220 | ||||||||
\(355\) | −7.12503 | −0.378157 | ||||||||
\(356\) | 17.1896 | 0.911045 | ||||||||
\(357\) | −0.391286 | −0.0207091 | ||||||||
\(358\) | −24.1933 | −1.27866 | ||||||||
\(359\) | 24.9326 | 1.31589 | 0.657945 | − | 0.753066i | \(-0.271426\pi\) | ||||
0.657945 | + | 0.753066i | \(0.271426\pi\) | |||||||
\(360\) | −7.96975 | −0.420043 | ||||||||
\(361\) | −17.7990 | −0.936788 | ||||||||
\(362\) | −14.7633 | −0.775941 | ||||||||
\(363\) | −54.7318 | −2.87268 | ||||||||
\(364\) | −17.0789 | −0.895176 | ||||||||
\(365\) | −7.57368 | −0.396425 | ||||||||
\(366\) | 0.0633382 | 0.00331074 | ||||||||
\(367\) | 5.07470 | 0.264897 | 0.132448 | − | 0.991190i | \(-0.457716\pi\) | ||||
0.132448 | + | 0.991190i | \(0.457716\pi\) | |||||||
\(368\) | −7.04978 | −0.367495 | ||||||||
\(369\) | 1.36243 | 0.0709251 | ||||||||
\(370\) | −16.8962 | −0.878393 | ||||||||
\(371\) | 5.36784 | 0.278684 | ||||||||
\(372\) | 46.4066 | 2.40607 | ||||||||
\(373\) | 12.1357 | 0.628364 | 0.314182 | − | 0.949363i | \(-0.398270\pi\) | ||||
0.314182 | + | 0.949363i | \(0.398270\pi\) | |||||||
\(374\) | 1.08148 | 0.0559219 | ||||||||
\(375\) | −3.22748 | −0.166666 | ||||||||
\(376\) | −11.9366 | −0.615584 | ||||||||
\(377\) | 52.4906 | 2.70340 | ||||||||
\(378\) | 38.0745 | 1.95834 | ||||||||
\(379\) | −33.1978 | −1.70525 | −0.852627 | − | 0.522519i | \(-0.824992\pi\) | ||||
−0.852627 | + | 0.522519i | \(0.824992\pi\) | |||||||
\(380\) | 2.74660 | 0.140898 | ||||||||
\(381\) | 6.03303 | 0.309081 | ||||||||
\(382\) | −10.4116 | −0.532702 | ||||||||
\(383\) | 13.5513 | 0.692437 | 0.346219 | − | 0.938154i | \(-0.387466\pi\) | ||||
0.346219 | + | 0.938154i | \(0.387466\pi\) | |||||||
\(384\) | −26.8567 | −1.37052 | ||||||||
\(385\) | −6.65313 | −0.339075 | ||||||||
\(386\) | −6.63904 | −0.337918 | ||||||||
\(387\) | 65.4488 | 3.32695 | ||||||||
\(388\) | 5.89524 | 0.299286 | ||||||||
\(389\) | −29.1973 | −1.48036 | −0.740181 | − | 0.672407i | \(-0.765260\pi\) | ||||
−0.740181 | + | 0.672407i | \(0.765260\pi\) | |||||||
\(390\) | −37.1056 | −1.87891 | ||||||||
\(391\) | 0.248691 | 0.0125768 | ||||||||
\(392\) | 5.82073 | 0.293991 | ||||||||
\(393\) | 37.1734 | 1.87515 | ||||||||
\(394\) | 32.1722 | 1.62081 | ||||||||
\(395\) | 15.5923 | 0.784535 | ||||||||
\(396\) | −98.2830 | −4.93891 | ||||||||
\(397\) | 3.26900 | 0.164066 | 0.0820332 | − | 0.996630i | \(-0.473859\pi\) | ||||
0.0820332 | + | 0.996630i | \(0.473859\pi\) | |||||||
\(398\) | −48.7146 | −2.44184 | ||||||||
\(399\) | −4.45056 | −0.222806 | ||||||||
\(400\) | −2.73133 | −0.136566 | ||||||||
\(401\) | −26.8559 | −1.34112 | −0.670559 | − | 0.741857i | \(-0.733946\pi\) | ||||
−0.670559 | + | 0.741857i | \(0.733946\pi\) | |||||||
\(402\) | −23.7373 | −1.18391 | ||||||||
\(403\) | 31.0719 | 1.54780 | ||||||||
\(404\) | −5.94038 | −0.295545 | ||||||||
\(405\) | 23.7567 | 1.18048 | ||||||||
\(406\) | 25.8875 | 1.28478 | ||||||||
\(407\) | −42.0860 | −2.08613 | ||||||||
\(408\) | 0.334164 | 0.0165436 | ||||||||
\(409\) | −35.7439 | −1.76742 | −0.883711 | − | 0.468033i | \(-0.844963\pi\) | ||||
−0.883711 | + | 0.468033i | \(0.844963\pi\) | |||||||
\(410\) | −0.389952 | −0.0192584 | ||||||||
\(411\) | 2.15448 | 0.106273 | ||||||||
\(412\) | 42.1106 | 2.07464 | ||||||||
\(413\) | −0.916454 | −0.0450958 | ||||||||
\(414\) | −40.6363 | −1.99717 | ||||||||
\(415\) | 10.1024 | 0.495909 | ||||||||
\(416\) | −43.0410 | −2.11026 | ||||||||
\(417\) | −28.9957 | −1.41992 | ||||||||
\(418\) | 12.3009 | 0.601657 | ||||||||
\(419\) | −12.9463 | −0.632470 | −0.316235 | − | 0.948681i | \(-0.602419\pi\) | ||||
−0.316235 | + | 0.948681i | \(0.602419\pi\) | |||||||
\(420\) | −10.1778 | −0.496626 | ||||||||
\(421\) | 23.5042 | 1.14552 | 0.572762 | − | 0.819721i | \(-0.305872\pi\) | ||||
0.572762 | + | 0.819721i | \(0.305872\pi\) | |||||||
\(422\) | −4.99810 | −0.243304 | ||||||||
\(423\) | 82.3857 | 4.00573 | ||||||||
\(424\) | −4.58421 | −0.222629 | ||||||||
\(425\) | 0.0963515 | 0.00467374 | ||||||||
\(426\) | −48.8154 | −2.36511 | ||||||||
\(427\) | 0.0116324 | 0.000562930 0 | ||||||||
\(428\) | −40.6066 | −1.96280 | ||||||||
\(429\) | −92.4245 | −4.46230 | ||||||||
\(430\) | −18.7327 | −0.903370 | ||||||||
\(431\) | −3.56689 | −0.171811 | −0.0859056 | − | 0.996303i | \(-0.527378\pi\) | ||||
−0.0859056 | + | 0.996303i | \(0.527378\pi\) | |||||||
\(432\) | 38.9341 | 1.87322 | ||||||||
\(433\) | −3.60278 | −0.173139 | −0.0865693 | − | 0.996246i | \(-0.527590\pi\) | ||||
−0.0865693 | + | 0.996246i | \(0.527590\pi\) | |||||||
\(434\) | 15.3241 | 0.735582 | ||||||||
\(435\) | 31.2807 | 1.49979 | ||||||||
\(436\) | −36.2466 | −1.73590 | ||||||||
\(437\) | 2.82865 | 0.135313 | ||||||||
\(438\) | −51.8892 | −2.47936 | ||||||||
\(439\) | 24.8183 | 1.18451 | 0.592256 | − | 0.805750i | \(-0.298237\pi\) | ||||
0.592256 | + | 0.805750i | \(0.298237\pi\) | |||||||
\(440\) | 5.68186 | 0.270872 | ||||||||
\(441\) | −40.1742 | −1.91306 | ||||||||
\(442\) | 1.10773 | 0.0526893 | ||||||||
\(443\) | −28.6854 | −1.36289 | −0.681443 | − | 0.731871i | \(-0.738647\pi\) | ||||
−0.681443 | + | 0.731871i | \(0.738647\pi\) | |||||||
\(444\) | −64.3822 | −3.05544 | ||||||||
\(445\) | 6.85878 | 0.325138 | ||||||||
\(446\) | −24.5867 | −1.16421 | ||||||||
\(447\) | −68.5807 | −3.24376 | ||||||||
\(448\) | −14.3536 | −0.678145 | ||||||||
\(449\) | −34.0314 | −1.60604 | −0.803020 | − | 0.595952i | \(-0.796775\pi\) | ||||
−0.803020 | + | 0.595952i | \(0.796775\pi\) | |||||||
\(450\) | −15.7439 | −0.742176 | ||||||||
\(451\) | −0.971313 | −0.0457373 | ||||||||
\(452\) | −13.3097 | −0.626034 | ||||||||
\(453\) | 9.37659 | 0.440551 | ||||||||
\(454\) | 20.6208 | 0.967781 | ||||||||
\(455\) | −6.81462 | −0.319474 | ||||||||
\(456\) | 3.80084 | 0.177990 | ||||||||
\(457\) | 38.9855 | 1.82367 | 0.911833 | − | 0.410562i | \(-0.134667\pi\) | ||||
0.911833 | + | 0.410562i | \(0.134667\pi\) | |||||||
\(458\) | −5.46386 | −0.255309 | ||||||||
\(459\) | −1.37346 | −0.0641075 | ||||||||
\(460\) | 6.46873 | 0.301606 | ||||||||
\(461\) | 19.9090 | 0.927255 | 0.463627 | − | 0.886030i | \(-0.346548\pi\) | ||||
0.463627 | + | 0.886030i | \(0.346548\pi\) | |||||||
\(462\) | −45.5822 | −2.12068 | ||||||||
\(463\) | 21.0581 | 0.978651 | 0.489325 | − | 0.872101i | \(-0.337243\pi\) | ||||
0.489325 | + | 0.872101i | \(0.337243\pi\) | |||||||
\(464\) | 26.4720 | 1.22893 | ||||||||
\(465\) | 18.5166 | 0.858688 | ||||||||
\(466\) | 26.2578 | 1.21637 | ||||||||
\(467\) | −2.19932 | −0.101772 | −0.0508862 | − | 0.998704i | \(-0.516205\pi\) | ||||
−0.0508862 | + | 0.998704i | \(0.516205\pi\) | |||||||
\(468\) | −100.669 | −4.65341 | ||||||||
\(469\) | −4.35948 | −0.201302 | ||||||||
\(470\) | −23.5803 | −1.08768 | ||||||||
\(471\) | 34.4175 | 1.58587 | ||||||||
\(472\) | 0.782665 | 0.0360251 | ||||||||
\(473\) | −46.6603 | −2.14544 | ||||||||
\(474\) | 106.827 | 4.90672 | ||||||||
\(475\) | 1.09592 | 0.0502842 | ||||||||
\(476\) | 0.303842 | 0.0139266 | ||||||||
\(477\) | 31.6399 | 1.44869 | ||||||||
\(478\) | −48.3349 | −2.21079 | ||||||||
\(479\) | 4.79525 | 0.219101 | 0.109550 | − | 0.993981i | \(-0.465059\pi\) | ||||
0.109550 | + | 0.993981i | \(0.465059\pi\) | |||||||
\(480\) | −25.6494 | −1.17073 | ||||||||
\(481\) | −43.1076 | −1.96554 | ||||||||
\(482\) | 4.59853 | 0.209457 | ||||||||
\(483\) | −10.4818 | −0.476940 | ||||||||
\(484\) | 42.5005 | 1.93184 | ||||||||
\(485\) | 2.35225 | 0.106810 | ||||||||
\(486\) | 71.9843 | 3.26527 | ||||||||
\(487\) | −31.9873 | −1.44948 | −0.724741 | − | 0.689021i | \(-0.758041\pi\) | ||||
−0.724741 | + | 0.689021i | \(0.758041\pi\) | |||||||
\(488\) | −0.00993420 | −0.000449700 0 | ||||||||
\(489\) | −39.9451 | −1.80638 | ||||||||
\(490\) | 11.4986 | 0.519455 | ||||||||
\(491\) | 14.1151 | 0.637007 | 0.318503 | − | 0.947922i | \(-0.396820\pi\) | ||||
0.318503 | + | 0.947922i | \(0.396820\pi\) | |||||||
\(492\) | −1.48589 | −0.0669892 | ||||||||
\(493\) | −0.933837 | −0.0420579 | ||||||||
\(494\) | 12.5995 | 0.566878 | ||||||||
\(495\) | −39.2158 | −1.76262 | ||||||||
\(496\) | 15.6701 | 0.703608 | ||||||||
\(497\) | −8.96518 | −0.402143 | ||||||||
\(498\) | 69.2143 | 3.10157 | ||||||||
\(499\) | −33.9271 | −1.51878 | −0.759392 | − | 0.650633i | \(-0.774504\pi\) | ||||
−0.759392 | + | 0.650633i | \(0.774504\pi\) | |||||||
\(500\) | 2.50621 | 0.112081 | ||||||||
\(501\) | 50.4673 | 2.25471 | ||||||||
\(502\) | 26.4365 | 1.17992 | ||||||||
\(503\) | −13.9526 | −0.622118 | −0.311059 | − | 0.950391i | \(-0.600684\pi\) | ||||
−0.311059 | + | 0.950391i | \(0.600684\pi\) | |||||||
\(504\) | −10.0281 | −0.446685 | ||||||||
\(505\) | −2.37026 | −0.105475 | ||||||||
\(506\) | 28.9708 | 1.28791 | ||||||||
\(507\) | −52.7107 | −2.34096 | ||||||||
\(508\) | −4.68478 | −0.207853 | ||||||||
\(509\) | 12.7429 | 0.564819 | 0.282410 | − | 0.959294i | \(-0.408866\pi\) | ||||
0.282410 | + | 0.959294i | \(0.408866\pi\) | |||||||
\(510\) | 0.660128 | 0.0292310 | ||||||||
\(511\) | −9.52970 | −0.421569 | ||||||||
\(512\) | −27.5764 | −1.21872 | ||||||||
\(513\) | −15.6219 | −0.689725 | ||||||||
\(514\) | −60.4548 | −2.66655 | ||||||||
\(515\) | 16.8025 | 0.740406 | ||||||||
\(516\) | −71.3799 | −3.14232 | ||||||||
\(517\) | −58.7351 | −2.58317 | ||||||||
\(518\) | −21.2599 | −0.934108 | ||||||||
\(519\) | 35.7516 | 1.56932 | ||||||||
\(520\) | 5.81978 | 0.255214 | ||||||||
\(521\) | −32.4044 | −1.41966 | −0.709831 | − | 0.704372i | \(-0.751229\pi\) | ||||
−0.709831 | + | 0.704372i | \(0.751229\pi\) | |||||||
\(522\) | 152.590 | 6.67867 | ||||||||
\(523\) | −4.56133 | −0.199453 | −0.0997265 | − | 0.995015i | \(-0.531797\pi\) | ||||
−0.0997265 | + | 0.995015i | \(0.531797\pi\) | |||||||
\(524\) | −28.8659 | −1.26101 | ||||||||
\(525\) | −4.06103 | −0.177238 | ||||||||
\(526\) | 38.8060 | 1.69202 | ||||||||
\(527\) | −0.552785 | −0.0240797 | ||||||||
\(528\) | −46.6113 | −2.02850 | ||||||||
\(529\) | −16.3380 | −0.710349 | ||||||||
\(530\) | −9.05593 | −0.393364 | ||||||||
\(531\) | −5.40189 | −0.234422 | ||||||||
\(532\) | 3.45595 | 0.149835 | ||||||||
\(533\) | −0.994890 | −0.0430935 | ||||||||
\(534\) | 46.9912 | 2.03351 | ||||||||
\(535\) | −16.2024 | −0.700491 | ||||||||
\(536\) | 3.72305 | 0.160811 | ||||||||
\(537\) | −36.7836 | −1.58733 | ||||||||
\(538\) | −15.4905 | −0.667843 | ||||||||
\(539\) | 28.6414 | 1.23367 | ||||||||
\(540\) | −35.7251 | −1.53736 | ||||||||
\(541\) | 1.74553 | 0.0750464 | 0.0375232 | − | 0.999296i | \(-0.488053\pi\) | ||||
0.0375232 | + | 0.999296i | \(0.488053\pi\) | |||||||
\(542\) | −27.8793 | −1.19752 | ||||||||
\(543\) | −22.4461 | −0.963255 | ||||||||
\(544\) | 0.765722 | 0.0328301 | ||||||||
\(545\) | −14.4627 | −0.619514 | ||||||||
\(546\) | −46.6887 | −1.99809 | ||||||||
\(547\) | 20.7430 | 0.886908 | 0.443454 | − | 0.896297i | \(-0.353753\pi\) | ||||
0.443454 | + | 0.896297i | \(0.353753\pi\) | |||||||
\(548\) | −1.67300 | −0.0714671 | ||||||||
\(549\) | 0.0685651 | 0.00292629 | ||||||||
\(550\) | 11.2243 | 0.478606 | ||||||||
\(551\) | −10.6216 | −0.452496 | ||||||||
\(552\) | 8.95164 | 0.381007 | ||||||||
\(553\) | 19.6193 | 0.834296 | ||||||||
\(554\) | −26.8342 | −1.14008 | ||||||||
\(555\) | −25.6890 | −1.09044 | ||||||||
\(556\) | 22.5158 | 0.954881 | ||||||||
\(557\) | −30.0010 | −1.27118 | −0.635591 | − | 0.772026i | \(-0.719244\pi\) | ||||
−0.635591 | + | 0.772026i | \(0.719244\pi\) | |||||||
\(558\) | 90.3256 | 3.82379 | ||||||||
\(559\) | −47.7929 | −2.02143 | ||||||||
\(560\) | −3.43674 | −0.145229 | ||||||||
\(561\) | 1.64428 | 0.0694216 | ||||||||
\(562\) | 15.2002 | 0.641183 | ||||||||
\(563\) | −38.1608 | −1.60829 | −0.804144 | − | 0.594435i | \(-0.797376\pi\) | ||||
−0.804144 | + | 0.594435i | \(0.797376\pi\) | |||||||
\(564\) | −89.8516 | −3.78343 | ||||||||
\(565\) | −5.31068 | −0.223422 | ||||||||
\(566\) | −6.85025 | −0.287938 | ||||||||
\(567\) | 29.8922 | 1.25535 | ||||||||
\(568\) | 7.65639 | 0.321255 | ||||||||
\(569\) | −32.9653 | −1.38198 | −0.690988 | − | 0.722866i | \(-0.742824\pi\) | ||||
−0.690988 | + | 0.722866i | \(0.742824\pi\) | |||||||
\(570\) | 7.50841 | 0.314493 | ||||||||
\(571\) | 1.51322 | 0.0633264 | 0.0316632 | − | 0.999499i | \(-0.489920\pi\) | ||||
0.0316632 | + | 0.999499i | \(0.489920\pi\) | |||||||
\(572\) | 71.7696 | 3.00084 | ||||||||
\(573\) | −15.8298 | −0.661298 | ||||||||
\(574\) | −0.490663 | −0.0204799 | ||||||||
\(575\) | 2.58108 | 0.107638 | ||||||||
\(576\) | −84.6052 | −3.52521 | ||||||||
\(577\) | 1.75534 | 0.0730758 | 0.0365379 | − | 0.999332i | \(-0.488367\pi\) | ||||
0.0365379 | + | 0.999332i | \(0.488367\pi\) | |||||||
\(578\) | 36.0676 | 1.50022 | ||||||||
\(579\) | −10.0940 | −0.419493 | ||||||||
\(580\) | −24.2901 | −1.00859 | ||||||||
\(581\) | 12.7116 | 0.527364 | ||||||||
\(582\) | 16.1159 | 0.668024 | ||||||||
\(583\) | −22.5570 | −0.934214 | ||||||||
\(584\) | 8.13850 | 0.336773 | ||||||||
\(585\) | −40.1677 | −1.66073 | ||||||||
\(586\) | −8.99210 | −0.371460 | ||||||||
\(587\) | 19.0952 | 0.788142 | 0.394071 | − | 0.919080i | \(-0.371066\pi\) | ||||
0.394071 | + | 0.919080i | \(0.371066\pi\) | |||||||
\(588\) | 43.8149 | 1.80690 | ||||||||
\(589\) | −6.28747 | −0.259071 | ||||||||
\(590\) | 1.54612 | 0.0636529 | ||||||||
\(591\) | 48.9147 | 2.01208 | ||||||||
\(592\) | −21.7399 | −0.893506 | ||||||||
\(593\) | −26.0877 | −1.07129 | −0.535646 | − | 0.844442i | \(-0.679932\pi\) | ||||
−0.535646 | + | 0.844442i | \(0.679932\pi\) | |||||||
\(594\) | −159.998 | −6.56481 | ||||||||
\(595\) | 0.121236 | 0.00497018 | ||||||||
\(596\) | 53.2544 | 2.18139 | ||||||||
\(597\) | −74.0657 | −3.03131 | ||||||||
\(598\) | 29.6740 | 1.21346 | ||||||||
\(599\) | 13.2440 | 0.541133 | 0.270567 | − | 0.962701i | \(-0.412789\pi\) | ||||
0.270567 | + | 0.962701i | \(0.412789\pi\) | |||||||
\(600\) | 3.46818 | 0.141588 | ||||||||
\(601\) | 19.8113 | 0.808120 | 0.404060 | − | 0.914733i | \(-0.367599\pi\) | ||||
0.404060 | + | 0.914733i | \(0.367599\pi\) | |||||||
\(602\) | −23.5707 | −0.960669 | ||||||||
\(603\) | −25.6962 | −1.04643 | ||||||||
\(604\) | −7.28113 | −0.296265 | ||||||||
\(605\) | 16.9581 | 0.689443 | ||||||||
\(606\) | −16.2393 | −0.659675 | ||||||||
\(607\) | 31.2565 | 1.26866 | 0.634331 | − | 0.773061i | \(-0.281275\pi\) | ||||
0.634331 | + | 0.773061i | \(0.281275\pi\) | |||||||
\(608\) | 8.70945 | 0.353215 | ||||||||
\(609\) | 39.3594 | 1.59492 | ||||||||
\(610\) | −0.0196246 | −0.000794578 0 | ||||||||
\(611\) | −60.1608 | −2.43385 | ||||||||
\(612\) | 1.79095 | 0.0723949 | ||||||||
\(613\) | 45.3983 | 1.83362 | 0.916810 | − | 0.399323i | \(-0.130755\pi\) | ||||
0.916810 | + | 0.399323i | \(0.130755\pi\) | |||||||
\(614\) | −5.31147 | −0.214354 | ||||||||
\(615\) | −0.592884 | −0.0239074 | ||||||||
\(616\) | 7.14929 | 0.288053 | ||||||||
\(617\) | −34.2262 | −1.37789 | −0.688947 | − | 0.724812i | \(-0.741927\pi\) | ||||
−0.688947 | + | 0.724812i | \(0.741927\pi\) | |||||||
\(618\) | 115.118 | 4.63073 | ||||||||
\(619\) | −11.4086 | −0.458549 | −0.229274 | − | 0.973362i | \(-0.573635\pi\) | ||||
−0.229274 | + | 0.973362i | \(0.573635\pi\) | |||||||
\(620\) | −14.3786 | −0.577457 | ||||||||
\(621\) | −36.7924 | −1.47643 | ||||||||
\(622\) | −15.1513 | −0.607513 | ||||||||
\(623\) | 8.63017 | 0.345760 | ||||||||
\(624\) | −47.7428 | −1.91124 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | −34.1522 | −1.36500 | ||||||||
\(627\) | 18.7023 | 0.746899 | ||||||||
\(628\) | −26.7259 | −1.06648 | ||||||||
\(629\) | 0.766907 | 0.0305786 | ||||||||
\(630\) | −19.8100 | −0.789251 | ||||||||
\(631\) | 41.9627 | 1.67051 | 0.835254 | − | 0.549864i | \(-0.185320\pi\) | ||||
0.835254 | + | 0.549864i | \(0.185320\pi\) | |||||||
\(632\) | −16.7551 | −0.666483 | ||||||||
\(633\) | −7.59911 | −0.302038 | ||||||||
\(634\) | −45.8433 | −1.82067 | ||||||||
\(635\) | −1.86927 | −0.0741796 | ||||||||
\(636\) | −34.5071 | −1.36830 | ||||||||
\(637\) | 29.3366 | 1.16236 | ||||||||
\(638\) | −108.786 | −4.30686 | ||||||||
\(639\) | −52.8438 | −2.09047 | ||||||||
\(640\) | 8.32125 | 0.328926 | ||||||||
\(641\) | 37.2796 | 1.47246 | 0.736228 | − | 0.676734i | \(-0.236605\pi\) | ||||
0.736228 | + | 0.676734i | \(0.236605\pi\) | |||||||
\(642\) | −111.007 | −4.38108 | ||||||||
\(643\) | 44.6128 | 1.75936 | 0.879679 | − | 0.475567i | \(-0.157757\pi\) | ||||
0.879679 | + | 0.475567i | \(0.157757\pi\) | |||||||
\(644\) | 8.13938 | 0.320736 | ||||||||
\(645\) | −28.4812 | −1.12145 | ||||||||
\(646\) | −0.224152 | −0.00881914 | ||||||||
\(647\) | 37.2753 | 1.46544 | 0.732721 | − | 0.680529i | \(-0.238250\pi\) | ||||
0.732721 | + | 0.680529i | \(0.238250\pi\) | |||||||
\(648\) | −25.5284 | −1.00285 | ||||||||
\(649\) | 3.85117 | 0.151171 | ||||||||
\(650\) | 11.4968 | 0.450940 | ||||||||
\(651\) | 23.2988 | 0.913153 | ||||||||
\(652\) | 31.0183 | 1.21477 | ||||||||
\(653\) | −16.1199 | −0.630819 | −0.315409 | − | 0.948956i | \(-0.602142\pi\) | ||||
−0.315409 | + | 0.948956i | \(0.602142\pi\) | |||||||
\(654\) | −99.0875 | −3.87463 | ||||||||
\(655\) | −11.5178 | −0.450036 | ||||||||
\(656\) | −0.501741 | −0.0195897 | ||||||||
\(657\) | −56.1713 | −2.19145 | ||||||||
\(658\) | −29.6703 | −1.15667 | ||||||||
\(659\) | 10.0809 | 0.392696 | 0.196348 | − | 0.980534i | \(-0.437092\pi\) | ||||
0.196348 | + | 0.980534i | \(0.437092\pi\) | |||||||
\(660\) | 42.7696 | 1.66480 | ||||||||
\(661\) | 5.28707 | 0.205643 | 0.102822 | − | 0.994700i | \(-0.467213\pi\) | ||||
0.102822 | + | 0.994700i | \(0.467213\pi\) | |||||||
\(662\) | −33.0352 | −1.28395 | ||||||||
\(663\) | 1.68419 | 0.0654087 | ||||||||
\(664\) | −10.8558 | −0.421288 | ||||||||
\(665\) | 1.37896 | 0.0534736 | ||||||||
\(666\) | −125.313 | −4.85579 | ||||||||
\(667\) | −25.0158 | −0.968614 | ||||||||
\(668\) | −39.1890 | −1.51627 | ||||||||
\(669\) | −37.3816 | −1.44526 | ||||||||
\(670\) | 7.35475 | 0.284139 | ||||||||
\(671\) | −0.0488820 | −0.00188707 | ||||||||
\(672\) | −32.2737 | −1.24499 | ||||||||
\(673\) | 30.5104 | 1.17609 | 0.588045 | − | 0.808828i | \(-0.299898\pi\) | ||||
0.588045 | + | 0.808828i | \(0.299898\pi\) | |||||||
\(674\) | 52.2971 | 2.01441 | ||||||||
\(675\) | −14.2546 | −0.548661 | ||||||||
\(676\) | 40.9310 | 1.57427 | ||||||||
\(677\) | −35.3014 | −1.35674 | −0.678372 | − | 0.734719i | \(-0.737314\pi\) | ||||
−0.678372 | + | 0.734719i | \(0.737314\pi\) | |||||||
\(678\) | −36.3847 | −1.39735 | ||||||||
\(679\) | 2.95976 | 0.113585 | ||||||||
\(680\) | −0.103537 | −0.00397046 | ||||||||
\(681\) | 31.3518 | 1.20141 | ||||||||
\(682\) | −64.3957 | −2.46584 | ||||||||
\(683\) | 10.7946 | 0.413044 | 0.206522 | − | 0.978442i | \(-0.433785\pi\) | ||||
0.206522 | + | 0.978442i | \(0.433785\pi\) | |||||||
\(684\) | 20.3706 | 0.778888 | ||||||||
\(685\) | −0.667543 | −0.0255055 | ||||||||
\(686\) | 33.1655 | 1.26626 | ||||||||
\(687\) | −8.30726 | −0.316942 | ||||||||
\(688\) | −24.1028 | −0.918912 | ||||||||
\(689\) | −23.1045 | −0.880212 | ||||||||
\(690\) | 17.6836 | 0.673204 | ||||||||
\(691\) | −16.3414 | −0.621655 | −0.310827 | − | 0.950466i | \(-0.600606\pi\) | ||||
−0.310827 | + | 0.950466i | \(0.600606\pi\) | |||||||
\(692\) | −27.7619 | −1.05535 | ||||||||
\(693\) | −49.3439 | −1.87442 | ||||||||
\(694\) | −13.4274 | −0.509697 | ||||||||
\(695\) | 8.98399 | 0.340782 | ||||||||
\(696\) | −33.6135 | −1.27412 | ||||||||
\(697\) | 0.0176996 | 0.000670422 0 | ||||||||
\(698\) | 27.2673 | 1.03208 | ||||||||
\(699\) | 39.9224 | 1.51000 | ||||||||
\(700\) | 3.15348 | 0.119190 | ||||||||
\(701\) | 8.14575 | 0.307661 | 0.153830 | − | 0.988097i | \(-0.450839\pi\) | ||||
0.153830 | + | 0.988097i | \(0.450839\pi\) | |||||||
\(702\) | −163.882 | −6.18533 | ||||||||
\(703\) | 8.72293 | 0.328991 | ||||||||
\(704\) | 60.3174 | 2.27330 | ||||||||
\(705\) | −35.8516 | −1.35025 | ||||||||
\(706\) | −8.99329 | −0.338467 | ||||||||
\(707\) | −2.98242 | −0.112165 | ||||||||
\(708\) | 5.89142 | 0.221413 | ||||||||
\(709\) | −41.0461 | −1.54152 | −0.770759 | − | 0.637126i | \(-0.780123\pi\) | ||||
−0.770759 | + | 0.637126i | \(0.780123\pi\) | |||||||
\(710\) | 15.1249 | 0.567627 | ||||||||
\(711\) | 115.643 | 4.33694 | ||||||||
\(712\) | −7.37028 | −0.276213 | ||||||||
\(713\) | −14.8081 | −0.554568 | ||||||||
\(714\) | 0.830616 | 0.0310850 | ||||||||
\(715\) | 28.6367 | 1.07095 | ||||||||
\(716\) | 28.5632 | 1.06746 | ||||||||
\(717\) | −73.4884 | −2.74447 | ||||||||
\(718\) | −52.9264 | −1.97520 | ||||||||
\(719\) | −8.18794 | −0.305359 | −0.152679 | − | 0.988276i | \(-0.548790\pi\) | ||||
−0.152679 | + | 0.988276i | \(0.548790\pi\) | |||||||
\(720\) | −20.2573 | −0.754945 | ||||||||
\(721\) | 21.1420 | 0.787369 | ||||||||
\(722\) | 37.7834 | 1.40615 | ||||||||
\(723\) | 6.99161 | 0.260021 | ||||||||
\(724\) | 17.4299 | 0.647777 | ||||||||
\(725\) | −9.69197 | −0.359951 | ||||||||
\(726\) | 116.184 | 4.31199 | ||||||||
\(727\) | 8.45191 | 0.313464 | 0.156732 | − | 0.987641i | \(-0.449904\pi\) | ||||
0.156732 | + | 0.987641i | \(0.449904\pi\) | |||||||
\(728\) | 7.32283 | 0.271402 | ||||||||
\(729\) | 38.1750 | 1.41389 | ||||||||
\(730\) | 16.0773 | 0.595047 | ||||||||
\(731\) | 0.850262 | 0.0314481 | ||||||||
\(732\) | −0.0747786 | −0.00276390 | ||||||||
\(733\) | −32.6343 | −1.20538 | −0.602688 | − | 0.797977i | \(-0.705904\pi\) | ||||
−0.602688 | + | 0.797977i | \(0.705904\pi\) | |||||||
\(734\) | −10.7725 | −0.397620 | ||||||||
\(735\) | 17.4825 | 0.644853 | ||||||||
\(736\) | 20.5123 | 0.756093 | ||||||||
\(737\) | 18.3196 | 0.674811 | ||||||||
\(738\) | −2.89214 | −0.106461 | ||||||||
\(739\) | −38.9034 | −1.43108 | −0.715542 | − | 0.698570i | \(-0.753820\pi\) | ||||
−0.715542 | + | 0.698570i | \(0.753820\pi\) | |||||||
\(740\) | 19.9481 | 0.733307 | ||||||||
\(741\) | 19.1563 | 0.703724 | ||||||||
\(742\) | −11.3948 | −0.418315 | ||||||||
\(743\) | −35.0291 | −1.28509 | −0.642547 | − | 0.766246i | \(-0.722122\pi\) | ||||
−0.642547 | + | 0.766246i | \(0.722122\pi\) | |||||||
\(744\) | −19.8975 | −0.729478 | ||||||||
\(745\) | 21.2490 | 0.778502 | ||||||||
\(746\) | −25.7615 | −0.943196 | ||||||||
\(747\) | 74.9262 | 2.74141 | ||||||||
\(748\) | −1.27682 | −0.0466852 | ||||||||
\(749\) | −20.3869 | −0.744922 | ||||||||
\(750\) | 6.85125 | 0.250172 | ||||||||
\(751\) | 24.1673 | 0.881876 | 0.440938 | − | 0.897537i | \(-0.354646\pi\) | ||||
0.440938 | + | 0.897537i | \(0.354646\pi\) | |||||||
\(752\) | −30.3402 | −1.10639 | ||||||||
\(753\) | 40.1940 | 1.46475 | ||||||||
\(754\) | −111.426 | −4.05790 | ||||||||
\(755\) | −2.90523 | −0.105732 | ||||||||
\(756\) | −44.9517 | −1.63488 | ||||||||
\(757\) | −13.5261 | −0.491614 | −0.245807 | − | 0.969319i | \(-0.579053\pi\) | ||||
−0.245807 | + | 0.969319i | \(0.579053\pi\) | |||||||
\(758\) | 70.4717 | 2.55965 | ||||||||
\(759\) | 44.0473 | 1.59881 | ||||||||
\(760\) | −1.17765 | −0.0427178 | ||||||||
\(761\) | −14.6317 | −0.530398 | −0.265199 | − | 0.964194i | \(-0.585438\pi\) | ||||
−0.265199 | + | 0.964194i | \(0.585438\pi\) | |||||||
\(762\) | −12.8068 | −0.463942 | ||||||||
\(763\) | −18.1979 | −0.658809 | ||||||||
\(764\) | 12.2922 | 0.444715 | ||||||||
\(765\) | 0.714605 | 0.0258366 | ||||||||
\(766\) | −28.7664 | −1.03937 | ||||||||
\(767\) | 3.94465 | 0.142433 | ||||||||
\(768\) | −16.6239 | −0.599863 | ||||||||
\(769\) | −24.4642 | −0.882202 | −0.441101 | − | 0.897457i | \(-0.645412\pi\) | ||||
−0.441101 | + | 0.897457i | \(0.645412\pi\) | |||||||
\(770\) | 14.1231 | 0.508963 | ||||||||
\(771\) | −91.9155 | −3.31025 | ||||||||
\(772\) | 7.83822 | 0.282104 | ||||||||
\(773\) | 7.20675 | 0.259209 | 0.129604 | − | 0.991566i | \(-0.458629\pi\) | ||||
0.129604 | + | 0.991566i | \(0.458629\pi\) | |||||||
\(774\) | −138.934 | −4.99387 | ||||||||
\(775\) | −5.73717 | −0.206085 | ||||||||
\(776\) | −2.52767 | −0.0907382 | ||||||||
\(777\) | −32.3236 | −1.15960 | ||||||||
\(778\) | 61.9796 | 2.22208 | ||||||||
\(779\) | 0.201319 | 0.00721299 | ||||||||
\(780\) | 43.8078 | 1.56857 | ||||||||
\(781\) | 37.6739 | 1.34808 | ||||||||
\(782\) | −0.527917 | −0.0188783 | ||||||||
\(783\) | 138.156 | 4.93728 | ||||||||
\(784\) | 14.7950 | 0.528392 | ||||||||
\(785\) | −10.6639 | −0.380610 | ||||||||
\(786\) | −78.9110 | −2.81466 | ||||||||
\(787\) | 11.0720 | 0.394675 | 0.197337 | − | 0.980336i | \(-0.436771\pi\) | ||||
0.197337 | + | 0.980336i | \(0.436771\pi\) | |||||||
\(788\) | −37.9833 | −1.35310 | ||||||||
\(789\) | 59.0006 | 2.10048 | ||||||||
\(790\) | −33.0991 | −1.17761 | ||||||||
\(791\) | −6.68224 | −0.237593 | ||||||||
\(792\) | 42.1403 | 1.49739 | ||||||||
\(793\) | −0.0500686 | −0.00177799 | ||||||||
\(794\) | −6.93938 | −0.246269 | ||||||||
\(795\) | −13.7686 | −0.488323 | ||||||||
\(796\) | 57.5136 | 2.03852 | ||||||||
\(797\) | 23.6826 | 0.838882 | 0.419441 | − | 0.907782i | \(-0.362226\pi\) | ||||
0.419441 | + | 0.907782i | \(0.362226\pi\) | |||||||
\(798\) | 9.44757 | 0.334440 | ||||||||
\(799\) | 1.07029 | 0.0378643 | ||||||||
\(800\) | 7.94717 | 0.280975 | ||||||||
\(801\) | 50.8692 | 1.79737 | ||||||||
\(802\) | 57.0092 | 2.01306 | ||||||||
\(803\) | 40.0461 | 1.41320 | ||||||||
\(804\) | 28.0249 | 0.988361 | ||||||||
\(805\) | 3.24768 | 0.114466 | ||||||||
\(806\) | −65.9589 | −2.32330 | ||||||||
\(807\) | −23.5518 | −0.829062 | ||||||||
\(808\) | 2.54703 | 0.0896042 | ||||||||
\(809\) | −5.48103 | −0.192703 | −0.0963513 | − | 0.995347i | \(-0.530717\pi\) | ||||
−0.0963513 | + | 0.995347i | \(0.530717\pi\) | |||||||
\(810\) | −50.4303 | −1.77194 | ||||||||
\(811\) | −4.58657 | −0.161056 | −0.0805281 | − | 0.996752i | \(-0.525661\pi\) | ||||
−0.0805281 | + | 0.996752i | \(0.525661\pi\) | |||||||
\(812\) | −30.5634 | −1.07257 | ||||||||
\(813\) | −42.3877 | −1.48660 | ||||||||
\(814\) | 89.3395 | 3.13135 | ||||||||
\(815\) | 12.3766 | 0.433532 | ||||||||
\(816\) | 0.849369 | 0.0297339 | ||||||||
\(817\) | 9.67102 | 0.338346 | ||||||||
\(818\) | 75.8766 | 2.65296 | ||||||||
\(819\) | −50.5416 | −1.76607 | ||||||||
\(820\) | 0.460387 | 0.0160774 | ||||||||
\(821\) | −9.89963 | −0.345499 | −0.172750 | − | 0.984966i | \(-0.555265\pi\) | ||||
−0.172750 | + | 0.984966i | \(0.555265\pi\) | |||||||
\(822\) | −4.57350 | −0.159519 | ||||||||
\(823\) | −13.3376 | −0.464919 | −0.232459 | − | 0.972606i | \(-0.574677\pi\) | ||||
−0.232459 | + | 0.972606i | \(0.574677\pi\) | |||||||
\(824\) | −18.0556 | −0.628995 | ||||||||
\(825\) | 17.0654 | 0.594142 | ||||||||
\(826\) | 1.94543 | 0.0676903 | ||||||||
\(827\) | −2.71638 | −0.0944576 | −0.0472288 | − | 0.998884i | \(-0.515039\pi\) | ||||
−0.0472288 | + | 0.998884i | \(0.515039\pi\) | |||||||
\(828\) | 47.9763 | 1.66729 | ||||||||
\(829\) | 22.0724 | 0.766607 | 0.383303 | − | 0.923623i | \(-0.374786\pi\) | ||||
0.383303 | + | 0.923623i | \(0.374786\pi\) | |||||||
\(830\) | −21.4453 | −0.744377 | ||||||||
\(831\) | −40.7987 | −1.41529 | ||||||||
\(832\) | 61.7816 | 2.14189 | ||||||||
\(833\) | −0.521914 | −0.0180832 | ||||||||
\(834\) | 61.5515 | 2.13136 | ||||||||
\(835\) | −15.6367 | −0.541132 | ||||||||
\(836\) | −14.5228 | −0.502280 | ||||||||
\(837\) | 81.7813 | 2.82678 | ||||||||
\(838\) | 27.4823 | 0.949359 | ||||||||
\(839\) | −51.7389 | −1.78623 | −0.893113 | − | 0.449832i | \(-0.851484\pi\) | ||||
−0.893113 | + | 0.449832i | \(0.851484\pi\) | |||||||
\(840\) | 4.36388 | 0.150568 | ||||||||
\(841\) | 64.9344 | 2.23912 | ||||||||
\(842\) | −49.8943 | −1.71947 | ||||||||
\(843\) | 23.1105 | 0.795966 | ||||||||
\(844\) | 5.90088 | 0.203117 | ||||||||
\(845\) | 16.3318 | 0.561832 | ||||||||
\(846\) | −174.887 | −6.01274 | ||||||||
\(847\) | 21.3377 | 0.733173 | ||||||||
\(848\) | −11.6520 | −0.400132 | ||||||||
\(849\) | −10.4151 | −0.357446 | ||||||||
\(850\) | −0.204533 | −0.00701544 | ||||||||
\(851\) | 20.5440 | 0.704240 | ||||||||
\(852\) | 57.6326 | 1.97446 | ||||||||
\(853\) | 21.9675 | 0.752154 | 0.376077 | − | 0.926588i | \(-0.377273\pi\) | ||||
0.376077 | + | 0.926588i | \(0.377273\pi\) | |||||||
\(854\) | −0.0246930 | −0.000844977 0 | ||||||||
\(855\) | 8.12803 | 0.277973 | ||||||||
\(856\) | 17.4107 | 0.595086 | ||||||||
\(857\) | 36.4401 | 1.24477 | 0.622386 | − | 0.782711i | \(-0.286164\pi\) | ||||
0.622386 | + | 0.782711i | \(0.286164\pi\) | |||||||
\(858\) | 196.197 | 6.69806 | ||||||||
\(859\) | 36.3576 | 1.24050 | 0.620252 | − | 0.784402i | \(-0.287030\pi\) | ||||
0.620252 | + | 0.784402i | \(0.287030\pi\) | |||||||
\(860\) | 22.1163 | 0.754158 | ||||||||
\(861\) | −0.746005 | −0.0254238 | ||||||||
\(862\) | 7.57174 | 0.257895 | ||||||||
\(863\) | 8.07008 | 0.274709 | 0.137354 | − | 0.990522i | \(-0.456140\pi\) | ||||
0.137354 | + | 0.990522i | \(0.456140\pi\) | |||||||
\(864\) | −113.284 | −3.85400 | ||||||||
\(865\) | −11.0772 | −0.376637 | ||||||||
\(866\) | 7.64792 | 0.259887 | ||||||||
\(867\) | 54.8372 | 1.86237 | ||||||||
\(868\) | −18.0920 | −0.614084 | ||||||||
\(869\) | −82.4450 | −2.79675 | ||||||||
\(870\) | −66.4021 | −2.25124 | ||||||||
\(871\) | 18.7643 | 0.635803 | ||||||||
\(872\) | 15.5413 | 0.526294 | ||||||||
\(873\) | 17.4458 | 0.590452 | ||||||||
\(874\) | −6.00462 | −0.203109 | ||||||||
\(875\) | 1.25827 | 0.0425371 | ||||||||
\(876\) | 61.2616 | 2.06984 | ||||||||
\(877\) | 49.0605 | 1.65666 | 0.828328 | − | 0.560243i | \(-0.189292\pi\) | ||||
0.828328 | + | 0.560243i | \(0.189292\pi\) | |||||||
\(878\) | −52.6839 | −1.77799 | ||||||||
\(879\) | −13.6716 | −0.461132 | ||||||||
\(880\) | 14.4420 | 0.486840 | ||||||||
\(881\) | 28.2067 | 0.950306 | 0.475153 | − | 0.879903i | \(-0.342393\pi\) | ||||
0.475153 | + | 0.879903i | \(0.342393\pi\) | |||||||
\(882\) | 85.2812 | 2.87157 | ||||||||
\(883\) | −11.9826 | −0.403248 | −0.201624 | − | 0.979463i | \(-0.564622\pi\) | ||||
−0.201624 | + | 0.979463i | \(0.564622\pi\) | |||||||
\(884\) | −1.30781 | −0.0439865 | ||||||||
\(885\) | 2.35073 | 0.0790189 | ||||||||
\(886\) | 60.8930 | 2.04574 | ||||||||
\(887\) | −0.691065 | −0.0232037 | −0.0116018 | − | 0.999933i | \(-0.503693\pi\) | ||||
−0.0116018 | + | 0.999933i | \(0.503693\pi\) | |||||||
\(888\) | 27.6048 | 0.926358 | ||||||||
\(889\) | −2.35203 | −0.0788847 | ||||||||
\(890\) | −14.5597 | −0.488043 | ||||||||
\(891\) | −125.614 | −4.20824 | ||||||||
\(892\) | 29.0276 | 0.971917 | ||||||||
\(893\) | 12.1737 | 0.407377 | ||||||||
\(894\) | 145.582 | 4.86899 | ||||||||
\(895\) | 11.3970 | 0.380959 | ||||||||
\(896\) | 10.4703 | 0.349789 | ||||||||
\(897\) | 45.1164 | 1.50639 | ||||||||
\(898\) | 72.2412 | 2.41072 | ||||||||
\(899\) | 55.6045 | 1.85451 | ||||||||
\(900\) | 18.5877 | 0.619589 | ||||||||
\(901\) | 0.411042 | 0.0136938 | ||||||||
\(902\) | 2.06189 | 0.0686533 | ||||||||
\(903\) | −35.8369 | −1.19258 | ||||||||
\(904\) | 5.70672 | 0.189803 | ||||||||
\(905\) | 6.95468 | 0.231181 | ||||||||
\(906\) | −19.9045 | −0.661282 | ||||||||
\(907\) | −14.7332 | −0.489209 | −0.244604 | − | 0.969623i | \(-0.578658\pi\) | ||||
−0.244604 | + | 0.969623i | \(0.578658\pi\) | |||||||
\(908\) | −24.3454 | −0.807930 | ||||||||
\(909\) | −17.5794 | −0.583072 | ||||||||
\(910\) | 14.4660 | 0.479542 | ||||||||
\(911\) | 2.58914 | 0.0857819 | 0.0428909 | − | 0.999080i | \(-0.486343\pi\) | ||||
0.0428909 | + | 0.999080i | \(0.486343\pi\) | |||||||
\(912\) | 9.66087 | 0.319903 | ||||||||
\(913\) | −53.4171 | −1.76785 | ||||||||
\(914\) | −82.7578 | −2.73739 | ||||||||
\(915\) | −0.0298373 | −0.000986391 0 | ||||||||
\(916\) | 6.45077 | 0.213139 | ||||||||
\(917\) | −14.4924 | −0.478581 | ||||||||
\(918\) | 2.91555 | 0.0962275 | ||||||||
\(919\) | −11.2402 | −0.370781 | −0.185390 | − | 0.982665i | \(-0.559355\pi\) | ||||
−0.185390 | + | 0.982665i | \(0.559355\pi\) | |||||||
\(920\) | −2.77357 | −0.0914418 | ||||||||
\(921\) | −8.07557 | −0.266099 | ||||||||
\(922\) | −42.2625 | −1.39184 | ||||||||
\(923\) | 38.5884 | 1.27015 | ||||||||
\(924\) | 53.8155 | 1.77040 | ||||||||
\(925\) | 7.95947 | 0.261706 | ||||||||
\(926\) | −44.7017 | −1.46899 | ||||||||
\(927\) | 124.618 | 4.09300 | ||||||||
\(928\) | −77.0238 | −2.52843 | ||||||||
\(929\) | 41.9325 | 1.37576 | 0.687881 | − | 0.725823i | \(-0.258541\pi\) | ||||
0.687881 | + | 0.725823i | \(0.258541\pi\) | |||||||
\(930\) | −39.3068 | −1.28892 | ||||||||
\(931\) | −5.93633 | −0.194556 | ||||||||
\(932\) | −31.0006 | −1.01546 | ||||||||
\(933\) | −23.0361 | −0.754169 | ||||||||
\(934\) | 4.66868 | 0.152764 | ||||||||
\(935\) | −0.509462 | −0.0166612 | ||||||||
\(936\) | 43.1632 | 1.41083 | ||||||||
\(937\) | 22.5067 | 0.735261 | 0.367630 | − | 0.929972i | \(-0.380169\pi\) | ||||
0.367630 | + | 0.929972i | \(0.380169\pi\) | |||||||
\(938\) | 9.25423 | 0.302161 | ||||||||
\(939\) | −51.9250 | −1.69451 | ||||||||
\(940\) | 27.8395 | 0.908025 | ||||||||
\(941\) | −45.7175 | −1.49035 | −0.745173 | − | 0.666871i | \(-0.767633\pi\) | ||||
−0.745173 | + | 0.666871i | \(0.767633\pi\) | |||||||
\(942\) | −73.0609 | −2.38045 | ||||||||
\(943\) | 0.474141 | 0.0154401 | ||||||||
\(944\) | 1.98936 | 0.0647480 | ||||||||
\(945\) | −17.9361 | −0.583462 | ||||||||
\(946\) | 99.0498 | 3.22039 | ||||||||
\(947\) | 36.7431 | 1.19399 | 0.596995 | − | 0.802245i | \(-0.296361\pi\) | ||||
0.596995 | + | 0.802245i | \(0.296361\pi\) | |||||||
\(948\) | −126.122 | −4.09627 | ||||||||
\(949\) | 41.0182 | 1.33151 | ||||||||
\(950\) | −2.32640 | −0.0754783 | ||||||||
\(951\) | −69.7002 | −2.26018 | ||||||||
\(952\) | −0.130277 | −0.00422230 | ||||||||
\(953\) | 46.8178 | 1.51658 | 0.758288 | − | 0.651919i | \(-0.226036\pi\) | ||||
0.758288 | + | 0.651919i | \(0.226036\pi\) | |||||||
\(954\) | −67.1646 | −2.17453 | ||||||||
\(955\) | 4.90468 | 0.158712 | ||||||||
\(956\) | 57.0653 | 1.84562 | ||||||||
\(957\) | −165.398 | −5.34655 | ||||||||
\(958\) | −10.1793 | −0.328878 | ||||||||
\(959\) | −0.839946 | −0.0271233 | ||||||||
\(960\) | 36.8174 | 1.18828 | ||||||||
\(961\) | 1.91514 | 0.0617786 | ||||||||
\(962\) | 91.5081 | 2.95034 | ||||||||
\(963\) | −120.167 | −3.87234 | ||||||||
\(964\) | −5.42914 | −0.174861 | ||||||||
\(965\) | 3.12752 | 0.100678 | ||||||||
\(966\) | 22.2507 | 0.715904 | ||||||||
\(967\) | 14.3053 | 0.460026 | 0.230013 | − | 0.973188i | \(-0.426123\pi\) | ||||
0.230013 | + | 0.973188i | \(0.426123\pi\) | |||||||
\(968\) | −18.2227 | −0.585701 | ||||||||
\(969\) | −0.340801 | −0.0109481 | ||||||||
\(970\) | −4.99332 | −0.160326 | ||||||||
\(971\) | −14.8605 | −0.476896 | −0.238448 | − | 0.971155i | \(-0.576639\pi\) | ||||
−0.238448 | + | 0.971155i | \(0.576639\pi\) | |||||||
\(972\) | −84.9864 | −2.72594 | ||||||||
\(973\) | 11.3042 | 0.362397 | ||||||||
\(974\) | 67.9021 | 2.17572 | ||||||||
\(975\) | 17.4797 | 0.559798 | ||||||||
\(976\) | −0.0252505 | −0.000808249 0 | ||||||||
\(977\) | −10.7287 | −0.343241 | −0.171621 | − | 0.985163i | \(-0.554900\pi\) | ||||
−0.171621 | + | 0.985163i | \(0.554900\pi\) | |||||||
\(978\) | 84.7948 | 2.71144 | ||||||||
\(979\) | −36.2661 | −1.15907 | ||||||||
\(980\) | −13.5756 | −0.433655 | ||||||||
\(981\) | −107.265 | −3.42470 | ||||||||
\(982\) | −29.9633 | −0.956169 | ||||||||
\(983\) | −48.6123 | −1.55049 | −0.775245 | − | 0.631660i | \(-0.782374\pi\) | ||||
−0.775245 | + | 0.631660i | \(0.782374\pi\) | |||||||
\(984\) | 0.637099 | 0.0203100 | ||||||||
\(985\) | −15.1557 | −0.482900 | ||||||||
\(986\) | 1.98233 | 0.0631303 | ||||||||
\(987\) | −45.1108 | −1.43589 | ||||||||
\(988\) | −14.8753 | −0.473246 | ||||||||
\(989\) | 22.7770 | 0.724265 | ||||||||
\(990\) | 83.2466 | 2.64575 | ||||||||
\(991\) | −3.88438 | −0.123392 | −0.0616958 | − | 0.998095i | \(-0.519651\pi\) | ||||
−0.0616958 | + | 0.998095i | \(0.519651\pi\) | |||||||
\(992\) | −45.5943 | −1.44762 | ||||||||
\(993\) | −50.2268 | −1.59390 | ||||||||
\(994\) | 19.0311 | 0.603631 | ||||||||
\(995\) | 22.9484 | 0.727514 | ||||||||
\(996\) | −81.7162 | −2.58928 | ||||||||
\(997\) | −36.4306 | −1.15377 | −0.576885 | − | 0.816825i | \(-0.695732\pi\) | ||||
−0.576885 | + | 0.816825i | \(0.695732\pi\) | |||||||
\(998\) | 72.0198 | 2.27975 | ||||||||
\(999\) | −113.459 | −3.58970 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 8035.2.a.b.1.19 | ✓ | 114 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8035.2.a.b.1.19 | ✓ | 114 | 1.1 | even | 1 | trivial |